This was captioned on Pintrest as coming from Popular Mechanics. However I think it's actually from Modern Mechanics.
The 'B.A.C." concept has nothing to do with the Lion-class, or the Admiralty, at all. Its actually from
The London Illustrated News, 20th June 1942 issue. The artist is that paper's regular naval artist, G. H. Davis. The design comes from Davis's own mind (and those infamous "anonymous naval experts" that always crop up to add some substance to an artist's fantasy).
It is purely a fantasy design, probably inspired by the events in the Mediterranean War up to that point. It has numerous technical flaws, not to mention the sliding landing deck extensions.
In the next issue, Davis added to the design four 50ft MTBs/MGBs in a hangar aft launched via the fantail, just to add some additional craziness.
The two images Tzoli posted above are from
The Hybrid Warship by R. D. Layman & Stephen McLaughlin, Conway Press, 1991.
The first is a double reconstruction, a sketch based on a sketch in Antony Preston's
Battleships 1856-1977 which was illustrating a hybrid Lion the DNC had drawn up in March 1941. This original sketch is lost. All we know is that all the main turrets were retained and the flight deck was too short. It had been the Controller, Rear Admiral Bruce Fraser who had asked the DNC, Goodall to base the hybrid design on Lion - Fraser pointedly rejected a hybrid based on Vanguard, presumably because she was more urgently wanted than the Lions.
Apparently the meeting hated the design. They proposed a Nelson-style arrangement of all turrets forward but they feared this would make the ship 50-55,000 tons. So it seems that the official design would have been a three-turret ship (A, B, Y layout). Preston's sketch was an illustration (I have never seen the 1977 original), we don't know what secondaries or dedicated carrier features were planned.
It was at this 12th March 1941 meeting that the Director of Plans proposed two quadruple turrets rather than the Nelson layout and sketched a doodle, which has ever since been interpreted - wrongly - as being based on Richelieu (which I have debunked elsewhere).
In any case by that September the official hybrid ship was dead.
The second drawing is based on a sketch by Rear Admiral Denis W Boyd, Flag Officer Mediterranean Aircraft Carriers. He submitted a report on 'Capital Ship Design' to Admiral Cunningham (C-in-C Med) in early 1942, no doubt heavily influenced by the destruction of Z Force a few weeks earlier. His proposal included a sketch of a hybrid battleship; 45,000 tons, 800 x 100 ft, 9x 15in or 16in guns, 16x 5.25in guns or smaller, an 80ft wide flight deck (wider if beam was increased to 110ft). It was simply a sketch and not with necessarily with Lion in mind at all. Cunningham sent the report to the Admiralty.
Goodall looked at it but as his own designs had been rejected as deeply flawed, this unsolicited design was of no interest.
It was three months later that Davis' 'B.A.C.' ship then appeared in
The London Illustrated News. It was the fad of the time and quickly faded away. But only that lost 1941 Goodall plan is the genuine Lion-based hybrid (two hybrid cruisers of the time also disappeared).